# Determining partial derivatives after coordinate transformation

I'm currently trying to figure out the partial deriviatives of a function, after there is a space transformation.

$$f(r_1, r_2, w) \rightarrow f(x, y, w)(2\sqrt{xy})^{-1}$$

Where $$r_1 = x^2 \\ \\ r_2 = y^2$$

How do I calculate the second partial derivatives, in this new transformed coordinates.

$$\frac{\partial^2 f(r_1, r_2, w)}{\partial r_1^2}, \ \ \ \ \ \frac{\partial^2 f(r_1, r_2, w)}{\partial r_2^2}, \ \ \ \ \ \frac{\partial^2 f(r_1, r_2, w)}{\partial w^2}$$